(a) A man travels from a village X on a bearing of 060° to a village Y which is 20km away. From Y, he travels to a village Z, on a bearing of 195°. If Z is directly east of X, calculate, correct to three significant figures, the distance of : (i) Y from Z ; (ii) Z from X . (b) An aircraft flies due South from an airfield on latitude 36°N, longitude 138°E to an airfield on latitude 36°S, longitude 138°E. (i) Calculate the distance travelled, correct to three significant figures ; (ii) if the speed of the aircraft is 800km per hour, calculate the time taken, correct to the nearest hour. [Take \(\pi = \frac{22}{7}\), R = 6400km].

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(a) A man travels from a village X on a bearing of 060° to a village Y which is 20km away. From Y, he travels to a village Z, on a bearing of 195°. If Z is directly east of X, calculate, correct to three significant figures, the distance of :
(i) Y from Z ; (ii) Z from X .
(b) An aircraft flies due South from an airfield on latitude 36°N, longitude 138°E to an airfield on latitude 36°S, longitude 138°E.
(i) Calculate the distance travelled, correct to three significant figures ; (ii) if the speed of the aircraft is 800km per hour, calculate the time taken, correct to the nearest hour.
[Take

π = \frac{22}{7}

, R = 6400km].

Explanation

(a) < XZY = 180° - (30° + 45°) = 105°

\frac{20}{\sin 105 °} = \frac{Y Z}{\sin 30 °}

Y Z = \frac{20 \sin 30 °}{\sin 105 °} = 10.35 k m

≊ 10.4 k m

(to 3 sig. figs)
(ii)

\frac{20}{\sin 75} = \frac{X Z}{\sin 45}

X Z = \frac{20 \sin 45}{\sin 75} = 14.64 k m

≊ 14.6 k m

( to 3 sig. figs)
(b) Let P and Q be two airfields.

Difference in latitude = 36° + 36° = 72°
(i) Distance between P and Q =

\frac{72}{360} \times 2 \times \frac{22}{7} \times 6400

\frac{22}{7} \times 2560

8, 045.71 k m ≊ 8, 050 k m

(3 sig. figs)
(ii) Time taken =

\frac{8, 045.71}{800} = 10.06 h o u r s

≊ 10 h o u r s

(to the nearest hour)

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(a) A man travels from a village X on a bearing of 060° to a village Y which is ...

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